A need exists to generate a near-millimeter wave radiation of moderate power from a fundamental input wave using solid-state devices in a phased array that combines the outputs of the devices with no ohmic contacts between devices in a two-dimensional grid.
Gallium arsenide Schottky barrier varactor diodes are the classical devices for frequency multiplication in the microwave region. During the last two decades efforts have been made to adapt this device for operation in the millimeter wave region. The most important improvement was the introduction of a moderately doped epitaxial layer on a heavily doped substrate for reduction of series resistance without loss of capacitance swing. However, the Schottky barrier varactor diode is still hampered by significant disadvantages, such as a substantial parasitic series resistance due to the ohmic back contact and the relatively long path from that contact to the active layer, especially when the skin effect becomes important. Another disadvantage is that the second harmonic is mainly generated so that for higher order multiplication expensive idler circuits must be provided.
Those disadvantages are overcome by the device disclosed in the aforesaid patent and illustrated schematically in FIG. 1a. It introduces the concept of back-to-back varactor diodes with electron blocking barriers (B) over a positive charge sheet, an intrinsic drift region (I), and a n.sup.+ doped region N.sup.+ that provides a back contact between the two BIN.sup.+ diodes. FIG. 1b is a diagram of its equivalent circuit. However, such a BIN.sup.+ device has its limitations; it is space charge limited.
The replacement of the Schottky barrier (which blocks only reverse current) by a barrier involving a positive charge sheet (which blocks also forward current) will enable the BIN.sup.+ device to reach the maximum capacitance without any external bias because it is already at an arbitrary reverse bias set by the positive charge sheet. When two such diodes are connected back to back in antiseries through the n.sup.+ doped region, a symmetrical capacitance-voltage (C-V) characteristic is obtained, and the structure generates only odd harmonics without idlers. Thus, by integrating two diodes back to back on one chip, back ohmic contacts are eliminated.
In contrast to conventional varactor diodes with a Schottky barrier, BIN.sup.+ diodes with a Mott or heterojunction barrier allow operation with a symmetric C-V characteristic of high Cmax/Cmin ratio by connecting two diodes back-to-back.
Each BIN.sup.+ back-to-back diode structure may be constructed, top to bottom, of Schottky metal contacts for external connections, a barrier layer with a thickness d.sub.bar .apprxeq.10 to 30 nm, a charge sheet of n-type doping, a drift region of intrinsic GaAs with a thickness d.sub.drift .apprxeq.50 . . . 150 nm, and an n.sup.+ layer internally connecting the two diodes in antiseries. As noted above, no bias is required as the sheet doping controls the operating point of the diodes. Thanks to the favorable structure geometry, the parasitic series resistance is minimal and does not degrade due to skin effect.
Lateral isolation from other devices on the same chip can be achieved by mesa etching and deposition of an insulating dielectric, such as SiO.sub.2. An additional light etch after metal deposition for surface contacts is recommended in order to reduce near-surface leakage between the metal contacts. The simple, high-yield planar process is appropriate for high-reliability hybrid integration of single devices with planar waveguide coupling and filter structures as well as for on-chip integration with planar antennas in quasi-optically coupled multidiode arrays.
The theoretical models presented here are not intended to be rigorous but rather to serve as guides to the prototype design of such structures. In this spirit, an intrinsic cut-off frequency is estimated for each type of diode from the minimum series capacitance of the drift layer, C'.sub.min, occurring in depletion and its maximum series resistance, R'.sub.max, occurring in accumulation, as EQU .omega..sub.ci =1/R'.sub.max C'.sub.min. (1)
Parasitic series resistance must be added to R'.sub.max for calculation of the extrinsic cut-off frequency. In reality, time averages of series capacitance and resistance affect the harmonic generation of the diodes making it dependent on the signal waveforms and thus on the embedding and driving conditions.
As noted above, when the drift region is intrinsic (I), electrons injected from the back contact layer (N.sup.+) carry a space charge limited current with a transit time limited frequency response. The C-V characteristic in this case has a steep transition, (dC/dV)/C=q/kT, between C.sub.min and C.sub.max enabling the "space charge varactor" to generate a frequency spectrum of high harmonic content suitable for triplers and higher order multipliers already at low power levels. With EQU C'.sub.min =.epsilon..sub.drift A/d.sub.drift ( 2)
and the high-field approximation EQU R'.sub.max =d.sup.2.sub.drift /2.epsilon..sub.drift V.sub.s A,(3)
one obtains EQU .omega..sub.ci =2v.sub.s /d.sub.drift' ( 4)
where A is the area of a single diode and v.sub.s is the effective electron saturation velocity, which may depend on d.sub.drift and the field distribution. As d.sub.drift /v.sub.s represents the average time needed by an electron to cross the drift region, the response of the BIN.sup.+ diode is transit-time limited and does not depend on the electron concentration. Estimates of the value of the average electron velocity in 100 nm GaAs layers range from 0.6.times.10.sup.7 cm/s for space averaging to 3.times.10.sup.7 cm/s for time averaging. A simulation for transit time devices gave values 1 to 2.times.10.sup.7 cm/s. Similar values have been calculated for Si. Table 1 lists the calculated intrinsic cut-off frequencies.
TABLE 1 ______________________________________ Calculated for d.sub.drift = 100 nm and N = 10.sup.17 /cm.sup.3 .eta./ .mu. (N) v.sub.s E.sub.crit (N) f.sub.ci (BIN) f.sub.ci (BNN) .eta..sub.o [cm.sub.2 /Vs] [cm/s] [kV/cm] [GHz] [THz] ______________________________________ Si 12 700 1 .times. 10.sup.7 15 300 1.5 GaAs 13 4500 1 to 2 to 4 300 to 8.6 2 .times. 10.sup.7 600 ______________________________________
The validity of the BIN.sup.+ concept of the aforesaid patent was proven with a single whisker-coupled SiO.sub.2 /Si diode operating as a frequency doubler in a waveguide mount and performing closely to the predictions of a large signal analysis for a stepfunction C-V.
FIG. 2 shows C-V characteristic curves from a pair of back-to-back BIN.sup.+ diodes with characteristic values related to physical diode properties. The maximum capacitance is reached when both diodes are in accumulation, whereas at the minimum capacitance one diode is in accumulation and the other fully depleted, leading to ##EQU1## with C.sub.bar =.epsilon..sub.bar A/d.sub.bar and C'.sub.min =.epsilon..sub.drift /d.sub.drift, where A is the area of each single diode, .epsilon..sub.BAR is the dielectric constant of the barrier and .epsilon..sub.drift is the dielectric constant of the drift region. The halfwidth of the C-V curve is close to 2V.sub..function., where V.sub..function. is called flatband voltage because at that voltage the field at the barrier is zero, marking the transition between accumulation and depletion of the drift region.
For the most general case of a trapezoidal barrier, as shown in FIG. 3, the flatband voltage V.sub..function. is determined by the following Equation (7) from the n-type doping sheet, N.sub.sheet, together with the barrier height at the metal interface, .PHI..sub.M, the barrier height at the interface with the drift material, .PHI..sub.D, and a and N.sup.+, the back contact layer, .PHI..sub.N+ (.apprxeq.0.1 V at room temperature). ##EQU2## with L.sub.D =.sqroot.2.epsilon..sub.drift kT/q.sup.2 n.sup.+ being the Debye length of the back contact layer N.sup.+. This formation covers several types of barriers which are listed in Table 2. In particular, this discussion refers tot he triangular barrier created by the doping sheet in all-GaAs material, i.e., .PHI..sub.D =0, as a Mott barrier.
TABLE 2 ______________________________________ Properties of various barriers Barrier m.sub.bar/ Type Material Drift Region .PHI..sub.M [V] .PHI..sub.D [V] m.sub.O ______________________________________ Mott GaAs GaAs 0.8 0 0.07 Hetero- AlGaAs GaAs 1.2 0.4 0.10 junction Hetero- AlAs GaAs :.tau. 2.0 1.0 0.15 junction :X 1.4 0.6 0.19 Oxide SiO.sub.2 Si 3.2 . . . 4.1 3/2 1.0 ______________________________________
As the capacitance changes, the series resistance also changes, as shown in FIG. 2. The maximum, EQU R.sub.max =2R'.sub.max +R.sub.N+' ( 9)
is the resistance of both drift regions of the back-to-back diodes in accumulation plus the parasitic series resistance, whereas the minimum EQU R.sub.min =R'.sub.max +R.sub.N+' ( 10)
is the resistance of only one accumulated diode plus parasitic because the other diode is fully depleted. As a reasonable average value R=1.5 R.sub.max '+R.sub.N+ has been used in the simulations.
FIG. 4 shows a simulated result for a tripler to 200 GHz. For a given halfwidth 2V.sub..function. the efficiency .eta. peaks at a certain input power with the peak shifting to higher powers, broadening and reaching a saturation value for larger halfwidths. Furthermore, the input power is related to the peak voltage drop over the capacitance V.sub.c' by P.sub.in .varies.V.sub.c. The condition for maximum efficiency, obtained from many simulations, can be described by ##EQU3## where 2V.sub..function. should be much larger than kT/q for a BIN+structure.
A discussion of what limits V.sub.c follows with reference to FIG. 5 where the conduction band edge of back-to-back BIN.sup.+ structure with Mott barriers and a 100 nm drift region has been plotted from a PISCES simulation depicting the situation 100 ps after the application of a large voltage step. (The solution after only 10 ps is practically identical as expected for a transit time of the order of 1 ps.) The steady-state solution differs by a decreased voltage drop over the forward biased barrier due to a substantial leakage conductance. The fields are high in the reverse biased diode and low in the forward biased diode as long as the input frequency is much smaller than the cut-off frequency.
The forward biased barrier exhibits a leakage current of density ##EQU4## which is caused by thermionic emission (TE) over the barrier with m.sub.bar being its effective mass and .PHI..sub.B its effective height. The leakage current in the reference biased barrier is dominated by Fowler-Nordheim (FN) tunneling with a density ##EQU5## which, in contrast to the thermionic current, is a
reverse leakage barrier E.sub.bar &gt;0. As a consequence, the current rises very sharply with the total applied voltage and will overtake the forward leakage current at a breakdown voltage. Beyond that voltage, the barriers would become highly rectifying in a sense that would lead to a build-up of charge between the barriers, which would shift the flatband voltage.
This functional breakdown voltage is estimated by equating the exponents of Equations (12) and (13). This leads to the barrier breakdown field ##EQU6## FIG. 5 shows by the solid line triangular peak the effective height of the Mott barrier (around 0.3 V). A dotted line shows the effective height of a heterojunction barrier to be higher and not so thin that current tunnels through the barrier. Thus, the above derivation of the breakdown holds not only for Mott (triangular) barriers but also for the trapezoidal heterojunction and oxide barriers as long as these barriers are not so thin that the current tunnels through the full barrier at breakdown, i.e., .PHI..sub.M -E.sub.bar,BD d.sub.bar .ltoreq.0 must be fulfilled. For these trapezoidal barriers, shown by a dotted line in FIG. 5, which leak only a little in forward direction, it is estimated that .PHI..sub.B .apprxeq..PHI..sub.D as the voltage drop over the forward biased diode will be about V.sub..function., which will usually be larger than .PHI..sub.M -.PHI..sub.D, of FIG. 3.
The breakdown voltage of a single diode is related to the barrier breakdown field by ##EQU7## Applying Q=.intg.CdV to the single and the back-to-back diodes, the breakdown voltage of the latter becomes ##EQU8## This derivation assumes that the voltage drop over the barriers is still determined by their capacitance rather than their conductance, which is a good approximation for heterojunction barriers at high frequency operation. (Note that V.sub.BD decreases with increase in sheet doping as illustrated by the dashed line in FIG. 5.)
Table 2 above lists the properties of various barriers starting with the simple GaAs Mott barrier, suitable only for low-power applications, and progressing to AlGaAs/GaAs with about 50% Al,AlAs/GaAs and SiO.sub.2 /Si. The Schottky barrier heights .PHI..sub.M of the III-V compounds have been estimated by the 2/3-bandgap rule. Note that tunneling through the X-valley is facilitated by the isotropic momentum distribution in the metal, which limits the advantage of a pure AlAs barrier.
With these parameters and the maximum allowed voltage drop over the capacitance, max(Vc), set equal to V.sub.BD, the results for the AlGaAs/GaAs heterojunction barrier tripler in the following Table 3 have been obtained. The area has been chosen to achieve matchable impedance levels.
TABLE 3 ______________________________________ Simulated Performance of a AlGaAs/GaAs BIN+ Tripler to 200 GHz ______________________________________ d.sub.bar [nm] 20 d.sub.drift [nm] 80 N.sub.sheet [cm.sup.-2 ] 5.5 .times. 10.sup.12 A [.mu.m.sup.2 ] 6 C.sub.max [fF] 15 C.sub.min [fF] 5 R [.OMEGA.] 20 2V.sub.f [V] 2.0 V.sub.c [V] 11.5 P.sub.in [mV] 19 .mu. [%] 35.5 P.sub.out [mV] 6.7 R.sub.1 [.OMEGA.] 48 X.sub.1 [.OMEGA.] 300 R.sub.3 [.OMEGA.] 35 X.sub.3 [.OMEGA.] 50 ______________________________________
Since already V.sub..function. .apprxeq.1V the effective height of the forward biased heterojunction barrier, .PHI..sub.B, was set to .PHI..sub.D. The area has been chosen to achieve matchable impedance levels.